Degenerate bilinear form
In mathematics, specifically linear algebra, a degenerate bilinear form f ( x , y ) {\displaystyle f(x,y)} on a vector space V {\displaystyle V} is a bilinear form such that the map from V {\displaystyle V} to V ∗ {\displaystyle V^{*}} (the dual space of V {\displaystyle V} ) given by v ↦ ( x ↦ f ( x , v ) ) {\displaystyle v\mapsto (x\mapsto f(x,v))} has a non-trivial kernel, i.e. there exist some non-zero x {\displaystyle x} in V {\displaystyle V} such that f ( x , y ) = 0 {\displaystyle f(x,y)=0} for all y ∈ V {\displaystyle y\in V} .